Finite Group DatabasebetaFinite Group Databasebeta| order | 11780 |
| isoclinism | isoclinic class of ΓL(1,𝔽32) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5×C19 · Schur multiplier (H2) = C2 |
| direct product | C22×C19×ΓL(1,𝔽32) |
| unambiguous semidirect product | (C22×C31)⋊(C5×C19) |
| unambiguous semidirect product | (C22×C19×C31)⋊C5 |
| Fitting, socle, Hall | C22×C19×C31 ⋊ C5 |
| derived, Sylow | C31 ⋊ C22×C5×C19 |
| Hall | C19×C31 ⋊ C22×C5 |
| Hall | C22×C31 ⋊ C5×C19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C19 | ΓL(1,𝔽32) |
| commutator, cosocle, hypocenter | C31 | C22×C5×C19 |
| Frattini | C1 | G |
| Fitting, socle | C22×C19×C31 | C5 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C22×C19 | |
40 conjugacy classes of subgroups.
836 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11780, 18);